Modelling J?V hysteresis in perovskite solar cells induced by voltage poling

We present an extension of the dynamic electrical model, which enable us to explain some important features of the perovskite solar cells (PSC), like the shape of the hysteresis and the appearance of the ?bump? in the so called reverse scan, without requiring any additional assumptions. We give analytical expressions in terms of the Lambert?s function W for the open circuit voltage, the stationary current, and the instantaneous current, which can be written also in terms of elementary functions for the most part of the ranges of the physical parameters. The initial polarization of the cell, modeled as the charging of a capacitor with voltage dependent capacitance, is consistently determined in the model, from the initial stationary conditions. This is inline with a previously observed sharp increase of the PSC capacitance beyond the open-circuit voltage. Besides the known features, we obtain characteristics that were not yet analyzed experimentally, like the change of the bump from the reverse scan branch of the J?V characteristic to the forward scan, with the increase of the poling voltage (or the increase of the PSC capacitance).